What is the RESOLVING POWER of a electron and light microscope?

The resolving power, also known as the resolution, of a microscope is a measure of its ability to distinguish fine details and separate two closely spaced objects. In both electron and light microscopes, the resolving power depends on the wavelength of the radiation used and the numerical aperture of the microscope's lens system.

For a light microscope, the resolving power is based on the properties of visible light waves, which have a wavelength range of approximately 400 to 700 nanometers (nm). Ernst Abbe, a German physicist, formulated a formula known as Abbe's formula to calculate the theoretical maximum resolution of a light microscope:

Resolution = 0.61 * (wavelength of light) / (numerical aperture of the lens system)

In practice, the resolution of a light microscope is typically limited to around 200-300 nm due to the diffraction of light waves.

On the other hand, an electron microscope uses a beam of electrons rather than visible light. The electron beam has a much shorter wavelength, typically in the range of 0.004 to 0.1 nm. The resolving power of an electron microscope can be calculated using a similar formula, derived by Ernst Ruska, who shared the Nobel Prize in Physics for his work on electron microscopy:

Resolution = 0.61 * (wavelength of electrons) / (numerical aperture of the lens system)

Due to the shorter wavelength of electrons, electron microscopes have much higher resolving power than light microscopes. They can achieve resolutions in the range of a few picometers (pm) or even sub-picometers, allowing researchers to observe extremely fine details of the specimen.

In summary, the resolving power of a light microscope is limited by the wavelength of visible light, while the resolving power of an electron microscope is determined by the much shorter wavelength of the electron beam.